Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T06:47:19.791Z Has data issue: false hasContentIssue false
  • English
  • Français

NEW DEVELOPMENT OF NONRIGID REGISTRATION

Published online by Cambridge University Press:  05 June 2014

HSI-YUE HSIAO ,
CHIH-YAO HSIEH ,
XI CHEN ,
YONGYI GONG ,
XIAONAN LUO  and
GUOJUN LIAO
HSI-YUE HSIAO
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA email hsiyue@gmail.com, josephsieh@gmail.com, chen.xi@mavs.uta.edu
CHIH-YAO HSIEH
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA email hsiyue@gmail.com, josephsieh@gmail.com, chen.xi@mavs.uta.edu
XI CHEN
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA email hsiyue@gmail.com, josephsieh@gmail.com, chen.xi@mavs.uta.edu
YONGYI GONG
Affiliation:
School of Information Technology, Guangdong Foreign Language and International Business University, Guangzhou, China
XIAONAN LUO
Affiliation:
National Engineering Research Center of Digital Life, School of Information Science & Technology, Sun Yat-sen University, Guangzhou, China
GUOJUN LIAO*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA email hsiyue@gmail.com, josephsieh@gmail.com, chen.xi@mavs.uta.edu National Engineering Research Center of Digital Life, School of Information Science & Technology, Sun Yat-sen University, Guangzhou, China
*
✉liao@uta.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We propose a new nonrigid registration algorithm which is based on the optimal control approach. In our previously proposed methods, the Jacobian determinant and the curl vector were used as control functions. In this algorithm, we use a new set of control functions. A main advantage of using the new controls is that the positivity and normalization of the Jacobian determinant are satisfied automatically. Numerical results on large deformation brain images are provided to show the accuracy and efficiency of the algorithm.

Keywords

nonrigid registrationoptimal controlbrain images

MSC classification

Secondary: 65K10: Optimization and variational techniques
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 3 , January 2014 , pp. 289 - 297
Copyright
Copyright © 2014 Australian Mathematical Society 

References

Auroux, D. and Fehrenbach, J., “Identification of velocity fields for geophysical fluids from a sequence of images”, INRIA, Rapport de recherche RR-6675, 2008.Google Scholar
Avants, B., Epstein, C., Grossman, M. and Gee, J., “Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain”, Medical Image Analysis 12 (2008) 26–41; doi:10.1016/j.media.2007.06.004.Google Scholar
Beg, M. F., Miller, M. I., Trouve, A. and Younes, L., “Computing large deformation metric mappings via geodesic flows of diffeomorphisms”, Int. J. Comput. Vis. 61 (2005) 139–157 ; doi:10.1023/B:VISI.0000043755.93987.aa.CrossRefGoogle Scholar
Chen, H.-M. C., Hsieh, C.-Y. and Liao, G., “Nonrigid image registration using adaptive grid generation: Preliminary results”, in: 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro (2007), 580–583; doi:10.1109/ISBI.2007.356918.Google Scholar
Chu, M.-Y., Chen, H.-M., Hsieh, C.-Y., Lin, T.-H., Hsiao, H.-Y., Liao, G. and Peng, Q., “Adaptive grid generation based nonrigid image registration using mutual information for breast MRI”, J. Signal Proc. Syst. 54 (2009) 45–63; doi:10.1007/s11265-008-0193-7.Google Scholar
Grajewski, M., Köster, M. and Turek, S., “Numerical analysis and implementational aspects of a new multilevel grid deformation method”, Appl. Numer. Math. 60 (2010) 767–781 ; doi:10.1016/j.apnum.2010.03.017.Google Scholar
Hsiao, H.-Y., Chen, H.-M., Lin, T.-H., Hsieh, C.-Y., Chu, M.-Y., Liao, G. and Zhong, H., “A new parametric nonrigid image registration method based on Helmholtz theorem”, in: Medical Imaging 2008: Image Processing, Volume 6914 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (eds Reinhardt, J. M. and Pluim, J. P. W.), (2008).Google Scholar
Hsieh, C.-Y., Chen, H.-M., Lin, T.-H., Hsiao, H.-Y., Chu, M.-Y., Liao, G. and Zhong, H., “On the development of a new nonrigid image registration using deformation based grid generation”, in: Medical Imaging 2008: Image Processing, Volume 6914 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (eds Reinhardt, J. M. and Pluim, J. P. W.), (2008); doi:10.1117/12.769811.Google Scholar
Kybic, J. and Unser, M., “Fast parametric elastic image registration”, IEEE Trans. Image Proc. 12 (2003) 1427–1442; doi:10.1109/TIP.2003.813139.CrossRefGoogle ScholarPubMed
Lee, E. and Gunzburger, M., “An optimal control formulation of an image registration problem”, J. Math. Imaging Vision 36 (2010) 69–80; doi:10.1007/s10851-009-0172-z.CrossRefGoogle Scholar
Lee, E. and Gunzburger, M., “Analysis of finite element discretization of an optimal control formulation of the image registration problem”, SIAM J. Numer. Anal. 49 (2011) 1321–1349; doi:10.1137/090767674.Google Scholar
Liao, G., Cai, X., Fleitas, D., Luo, X., Wang, J. and Xue, J., “Optimal control approach to data set alignment”, Appl. Math. Lett. 21 (2008) 898–905; doi:10.1016/j.aml.2007.09.011.CrossRefGoogle Scholar
Liao, G., Lei, Z. and de la Pena, G., “Adaptive grids for resolution enhancement”, Shock Waves 12 (2002) 153–156; doi:10.1007/s00193-002-0149-y.CrossRefGoogle Scholar
Liao, G., Liu, F., de la Pena, G. C., Peng, D. and Osher, S., “Level-set-based deformation methods for adaptive grids”, J. Comput. Phys. 159 (2000) 103–122; doi:10.1006/jcph.2000.6432.Google Scholar
Liu, J., “New developments of the deformation method”, Ph. D. Thesis, UT Arlington dissertation (2006).Google Scholar
Liu, F., Ji, S. and Liao, G., “An adaptive grid method and its application to steady Euler flow calculations”, SIAM J. Sci. Comput. 20 (1999) 811–825; doi:10.1137/S1064827596305738.Google Scholar
Rueckert, D., Aljabar, P., Heckemann, R. A., Hajnal, J. V. and Hammers, A., Diffeomorphic Registration Using B-Splines, Volume 4191 of Lect. Notes in Comput. Sci. (Springer, Berlin-Heidelberg, 2006), 702–709; doi:10.1007/11866763_86.Google Scholar